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URN

etd-0823111-121121

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Author

Jian-Jhang Chen

Author's Email Address

No Public.

Department

Mechanical Engineering

Year

2010

Semester

2

Degree

Master

Type of Document

Master's Thesis

Language

zh-TW.Big5 Chinese

Page Count

84

Title

Optimization by Entropy Approach for the Fin Arrangement of a Heat Sink

Keyword

entropy

effectiveness

fin

optimum

heat sink

heat sink

optimum

fin

effectiveness

entropy

Abstract

In this study, a theoretical analysis of a heat sink is presented to pursue the maximum thermal dissipation and the least material cost. Due to the general derivation, the longitudinal fin arrays on a heat sink can be arranged as either square, rectangular, equilaterally triangular, cylindrical, or annular cross-section. By inputting the dimensionless parameter, Biot number, shape parameter and the total mass, the heat balance equation is derived in transcendental form which can be solved by iterative method to calculate the optimum fin length. Meanwhile, the thermal resistance of a heat sink can be obtained to illustrate the cooling performance under various design conditions. This study presents a mathematical approach to calculate the total heat loss from a heat sink by summing up the fin spacing on the assign sink surface and the surface of rectangular fins, with each of them able to have its specified thermal conductivity and heat transfer coefficient. Meanwhile, the optimum equation with maximum heat dissipation is derived and solved to find the optimum configuration of fins in a heat sink by inputting the values of dimensionless parameters, Bi,γ, and M . Several cases including fin arrangements with various thermal conductivity distributions and heat transfer coefficients will be explored for practical application. During the computing process, in the first part, convective effect from the fin tip is not included to the impact of the heat transfer performance. In the second part, the convective effect will be included on the fin tip. The entropy generation is a unique concept that combines both the heat sink resistance and pressure drop. It can be obtained by combining a mass, force, energy, and entropy balance across a heat sink. It is a function of all system parameters considered in this study. By minimizing entropy generation with respect to each design variable, the overall thermal performance of a heat sink can be optimized. The entropy minimization is used to explore the thermal and fluid performance. In optimization process what is needed to know is the base area and the total mass. Thereafter, the optimum fin number and fin dimension can be obtained through this study. And these results can be used as reference for designer in the design of heat sink.